MetaAnalysis

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Meta-Analysis
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Steps of a systematic review

• Step 1 Framing question for a review
• Step 2 Identifying relevant literature
• Step 3 Assessing the quality of the literature
• Step 4 Summarizing the evidence
• Step 5 Interpreting the finding

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Definitions

• When an systematic review incorporates a specific
  statistical strategy for assembling the results
  of several studies into a single estimate.

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Summarizing the Evidence

• First Question Are the observed estimations are
  consistent among the included studies? (if not,
  why?)
• Is a statistical combination of individual
  effects is feasible?

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• The judgment that the studies should or should
  not be combined should be stated and justified
  explicitly. There is some of a tendency to make
  this judgment on the basis of the quantitative
  results, but its critical to make a qualitative
  judgment.

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Graphical Display

• The graphical display of results from individual
  studies on a common scale is a Forest plot.
• In the forest plot each study is represented
  by a black square and a horizontal line
  (CI95).The area of the black square reflects
  the weight of the study in the meta-analysis.
• Forest plot is an important step, which allows
  a visual examination of heterogeneity between
  studies.

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Odds Ratio
Line of no significance
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Odds Ratio with pooled effect size
Best/point estimate
Confidence Interval
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Forest Plot
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Forest Plot
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Possible cause of Heterogeneity

• 1- Due to chance
• 2- Due to scale used to measure the effect
• 3- Due to treatment characteristics
• 4- Due to patient level covariates
• 5- Unexplainable
• 6- Characteristics of the design and conduct of
  the studies.

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Assessing between study heterogeneity

• When effect sizes differ, but only due to chance
  error, the effect estimate considered to be
  homogenous (unique true effect).
• When the variability in effect sizes exceeds that
  expected from chance alone, and there are real
  differences between studies there are
  heterogeneity.

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Statistical Methods for Detection of
Heterogeneity

• This is a test that observed scatter of study
  outcomes is consistent with all of them
  estimating the same underlying effect.
• Q X2homo?i1nwi (Ti -T)2
• wi weight / Tmeta analytic estimate of
  effect Ti effect measure of each study
• It has very low statistical power. (cut off
  significance0.1)

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Exploration of heterogeneity and its sources
should be planned in advance.
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In a meta-analysis, documenting heterogeneity of
effect can be as important as reporting averages.
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A systematic review does not always have to have
a meta-analysis!

• We should proceed with meta-analysis only if the
  studies are similar in clinical characteristics
  and methodological quality, and are homogenous in
  effects.

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Meta-Analysis

• In a meta-analysis, the effects observed across
  studies are pooled to produce a weighted average
  effect of all the studies-the summary effect.
• Each study is weighted according to some measure
  of its importance.
• In most meta-analyses, this is achieved by
  assigning a weight to each study in inverse
  proportion to the variance of its effect.

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Fixed effect model

• In this model, all of the observed difference
  between the studies is due to chance
• Observed study effectFixed effect error

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General Fixed effect modelThe inverse variance
weighted method

• T? wiTi/ ? wi
• The weights that minimize the variance of T are
  inversely proportional to the conditional
  variance in each study
• Wi1/vi

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Random effect model

• Assume there are two component of variability
• 1)Due to inherent differences of the effect being
  sought in the studies (e.g. different design,
  different populations, different treatments,
  different adjustments ,etc.)
• 2)Due to sampling error

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Random effect model

• There are two separable effects that can be
  measured
• 1.The effect that each study is estimating
• 2.The common effect that all studies are
  estimating
• Observed study effectstudy specific (random
  )effect error

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• The random effect model, assumes a different
  underlying effect for each study.
• This model leads to relatively more weight being
  given to smaller studies and to wider confidence
  intervals than the fixed effects models.
• The use of this model has been advocated if there
  is heterogeneity between study results.

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• The random effect model may exaggerate the
  impact of publication bias and poor quality in
  smaller studies.

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• meta prevalence se, gr(r)
• Meta-analysis
• Pooled 95 CI
  Asymptotic No. of
• Method Est Lower Upper z_value
  p_value studies
• Fixed 0.380 0.373 0.387 104.108
  0.000 4
• Random 0.341 -0.151 0.832 1.357
  0.175
• Test for heterogeneity Q 1.3e04 on 3 degrees
  of freedom
• (p 0.000)

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Step 5

• Interpreting the finding

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• The principal findings should be related to the
  main question formulated in step1.
• Other finding should be considered secondary.

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Validity of the main finding

• Are the searches adequate?
• Is there a risk of publication and related
  biases?
• Is the quality of the included studies high
  enough?

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Funnel Plot

• Plots of the trials effect estimates against
  sample size, may be useful to assess the validity
  of meta-analyses
• A symmetrical shape is expected, since greater
  scatter in estimate is expected for smaller
  study.
• The cardinal sign of publication bias is a hole
  in the middle or one side of the plot, that is an
  area where we would expect to see study result
  but where there are apparently none.

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